Revisiting Mixture Policies in Entropy-Regularized Actor-Critic

In this paper, we study the role of the critic in actor--critic for entropy-regularized, finite, discounted environments. We establish that, when the critic is exact, using the latter as a baseline is a variance-reduction method in a strong sense. In this case, actor--critic with stochastic gradients matches the sample complexity of deterministic policy gradient, reaching an $ε$-optimal regularized value with $\tilde{O}(\log(1/ε))$ samples. In practice, the critic is learned alongside the actor: the variance of the actor update is then influenced by the critic's variance and bias. Specifically, when the critic has a sufficiently small error, the variance reduction and rapid convergence are preserved. This suggests to learn the critic first, keeping it up to date after each actor update, underscoring the crucial role of accurate critic estimation in actor--critic methods.

Expressive generative policies such as diffusion and flow models are appealing for MaxEnt online reinforcement learning because of their ability to model multimodal and highly non-Gaussian action distributions. However, training effective soft generative policies faces two obstacles that often arise together. First, marginal action densities are often unavailable, so existing methods typically rely on entropy bounds, heuristic proxies or approximations. Second, iterative shared-parameter samplers raise inference cost and require backpropagation through time over repeated network evaluations, increasing memory cost and destabilizing policy optimization. These obstacles motivate us to seek a generative policy that exposes a tractable MaxEnt objective while requiring only a single sampled actor forward pass for action generation. To this end, we propose soft generative actor-critic (SoftGAC), whose actor defines a stochastic bridge from a fixed base latent to a terminal action latent in pre-tanh space. This structured bridge allows us to lift the MaxEnt objective as an analytically tractable path-wise relative-entropy objective against a high-entropy reference process. In practical finite-step implementation, this relative entropy reduces exactly to sampled transition control energy and thus provides principled soft regularization. Moreover, we keep the single-pass actor lightweight by using small step-specific bridge transitions, each evaluated only once per sampled action, while maintaining a parameter budget comparable to strong actor baselines. Extensive experiments on challenging continuous-control benchmarks show that SoftGAC attains higher or competitive returns than strong generative policy baselines, including diffusion and flow-matching policies, while staying in the low-latency regime of one-pass actors and showing considerable improvements in the compute-return tradeoff.

Retry-based objectives such as pass@K and max@K optimize the best return obtained from multiple sampled trajectories, and recent work has shown that they can promote exploration without explicit exploration bonuses. In discrete action spaces, ReMax was shown to do so by adapting to return uncertainty. In this work, we introduce pathwise derivative estimators for retry objectives and use them to extend ReMax to continuous action spaces. We study the resulting learning dynamics and show that, even with deterministic rewards, ReMax can encourage stochastic exploration by reshaping the policy-gradient landscape. In particular, it alters gradients both in direction, biasing updates toward higher policy entropy, and in magnitude, damping gradients and slowing convergence. We further show that Adam's adaptive normalization can mitigate this damping, depending on its numerical stabilization parameter. Empirically, we instantiate this objective as ReMax Actor-Critic (ReMAC), an off-policy actor--critic algorithm that optimizes the ReMax objective using a pathwise derivative estimator. Our experiments show that ReMAC can promote higher policy entropy without entropy regularization and achieves performance comparable to SAC.